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Inequalities for elementary means. (Ungleichungen für elementare Mittelwerte.) (German) Zbl 0813.26009
Für die verschiedenen positiven Zahlen $$x$$ und $$y$$ seien $$G(x, y):= \sqrt{xy}$$, $$A(x, y):= (x+ y)/2$$, $$L(x, y):= (x- y)/(\ln x- \ln y)$$ und $$I(x, y):= e^{-1}(x^ x/ y^ y)^{1/(x- y)}$$. Gezeigt werden die Ungleichungen $L(x, y)< \sqrt{L(G(x, y)^ 2, A(x,y)^ 2)}< \sqrt{I(G(x, y)^ 2, A(x, y)^ 2)}< I(x, y).$ Die rechte Seite dieser Ungleichungskette sowie einige weitere Ungleichungen, werden unter Benutzung von Identitäten bewiesen.

##### MSC:
 26D15 Inequalities for sums, series and integrals
##### Keywords:
inequalities; means
Full Text:
##### References:
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